Proper account of auto-correlations improves decoding performances of state-space (semi) Markov models

State-space models are widely used in ecology to infer hidden behaviors. This study develops an extensive numerical simulation-estimation experiment to evaluate the state decoding accuracy of four simple state-space models. These models are obtained by combining different Markovian specifications (Markov and semi-Markov) for the hidden layer with the absence (model AR0) and presence (AR1) of auto-correlation for the observation layer. Model parameters are issued from two sets of real annotated trajectories. Three metrics are developed to help interpret model performance. The first is the Hellinger distance between Markov and semi-Markov sojourn time probability distributions. The second is sensitive to the overlap between the probability density functions of state-dependent variables (e.g., speed variables). The third quantifies the deterioration of the inference conditions between AR0 and AR1 formulations. It emerges that the most sensitive model choice concerns the auto-correlation of the random processes describing the state-dependent variables. Opting for the absence of auto-correlation in the model while the state-dependent variables are actually auto-correlated, is detrimental to state decoding performance. Regarding the hidden layer, imposing a Markov structure while the state process is semi-Markov (with negative Binomial sojourn times) does not impair the state decoding performances. The real-life estimates are consistent with our experimental finding that performance deteriorates when there are significant temporal correlations that are not accounted for in the model. In light of these findings, we recommend that researchers carefully consider the structure of the statistical model they suggest and confirm its alignment with the process being modeled, especially when considering the auto-correlation of observed variables.